Networks are pervasive in nature and technology, and as such form a highly relevant framework for our understanding of reality. Ecological systems, atoms in molecules and crystals, as well as human communication and transportation systems are but a few examples thereof. Quantum mechanics has forever changed our understanding of reality with its extraordinarily precise predictive power. Most research into networks so far has studied networks governed by classical correlations. These studies have revealed striking underlying laws and patterns which apply to a vast range of networks, in nature and in society. Quantum mechanics, however, allows for significantly stronger statistical correlations between constituent nodes and links of a hypothetical network. Ensembles of atoms, quantum information systems and even the entire universe may be viewed as networks with quantum properties. This project will strive to create a comprehensive formalism for the description and control of classical and quantum networks. We will furthermore devise tests for the presence of quantum effects in networks, and underpin our theoretical findings with targeted measurements on small physical quantum systems. With this formalism we expect that it will be possible to provide answers to numerous questions, such as: What is a quantum network? What properties does a network necessitate to display quantum behaviour? And what tests can we perform on a network to determine its quantum properties? The results of the project will have both fundamental and technological impact. It is known that security of communication channels can be vastly enhanced using quantum mechanical mechanisms. We will study what other enhancements are possible, for example in terms of information distribution and computational power of a network, when quantum mechanical correlations are allowed.

The CEU contribution will be to contribute to a fundamental, unified understanding of the topological and temporal aspect and the control principles of real networks, knowledge that will be applied, with the help of the other team members, to quantum networks. Besides establishing the theoretical framework, we aim to test work with the experimental groups to test our results experimentally, exploring the scalability and limitations of the theory in the construction, control and observation of real quantum networks. Hence specific emphasis will be do develop network topologies, and understand the expected classical behavior of networks, that offer the best quantitative comparison with quantum networks. The role of the CEU group will be to build on the wealth of experience on classical networks, to help the quantum theory group, and the experimental teams, discern classical from quantum effects.